\usepackage{amsmath,amssymb,amsfonts,graphicx,subfigure,bm,yfonts}
\usepackage[hidelinks]{hyperref}
\usepackage{cleveref,xcolor}
\usepackage{rotating}
%\usepackage[outdir=./]{epstopdf}

\usepackage{multirow}


%%%%%%%%%                              DEFINITIONS START

\def\cpar{$C_{ij},\rho$ parameterization~}
\def\hpar{h-parameterization~}

\newcommand{\todo}[1]{{\textbf {\color{red} #1}}}
\newcommand{\done}[1]{{\bf {\color{green} #1}}}
\newcommand{\connect}{{\textbf{\color{red} $<-$ Connect $->$ }}}


\def\rmrk#1{{\textbf{[[#1]]}}}
\def\rmrkok#1{}
%\def\eqref#1{\ref{#1}}
\def\eqrf#1{equation~\eqref{eq:#1}}
%\def\eqref#1{equation~\ref{eq:#1}}
\def\eq{equation~}
\def\figref#1{Figure~\ref{fig:#1}}
\def\figrefp#1{(Figure~\ref{fig:#1})}

\def\fref#1{\ref{#1}}

\def\rhoK{\hat{\rho}}
\def\cK{\hat{c}}


%\def\rmrk#1{{[\textcolor[rgb]{0,0,0.8}{#1}]}} % [blue]
%\def\rmrkm#1{{\textbf{[[\textcolor[rgb]{{1.00,0.00,0.00}}{#1}]]}}}
% _____________________________________________________________________________
\def\mainauthor{Vladimir Kazei}
\def\coauthorb{Ekkehart Tessmer}
\def\coauthorc{}%Zedong Wu
\def\coauthora{Tariq Alkhalifah}
% - my definitions==============================================================================================

\def\DP{Diffraction-based radiation 
patterns }
\def\dP{diffraction-based radiation 
patterns }

\def\nt{N}
\newcommand{\Mod}[1]{\ (\mathrm{mod}\ #1)}
\def\dv{\mathbf{d}}
\def\Amat{\mathbb{A}}
\def\Rmat{\mathbb{R}}
\def\Umat{\mathbb{U}}
\def\Smat{\mathbb{S}}
\def\Vmat{\mathbb{V}}
\def\SF{R}
\def\xv{\mathbf{x}}
\def\mv{\mathbf{m}}
%\def\tmul{\otimes}
\def\tmul{}
\def\cv{\mathbf{c}}

\def\sp{\varsigma}
\def\spv{\bm{\sp}}
\def\gp{\xi}
\def\gpv{\bm{\gp}}

\newcommand{\nmz}[1]{\mathbf{\bar{\text{$#1$}}}}
%\def\nmz#1{\mathbf{\bar #1}}

\def\Uv{\mathbf{U}}
\def\kv{\mathbf{k}}
\def\sv{\mathbf{s}}
\def\svn{\mathbf{\bar{\sv}}}
\def\Sv{\mathbf{S}}
\def\Gv{\mathbf{G}}
\def\Cv{\mathbf{C}}
\def\ev{\mathbf{e}}
\def\gv{\mathbf{g}}
\def\gvn{\mathbf{\bar{\gv}}}
\def\Av{\mathbf{A}}
\def\Bv{\mathbf{B}}
\def\uv{\mathbf{u}}
\def\rv{\mathbf{r}}
\def\dxv{\Delta \mathbf{x}}
\def\Kv{\mathbf{K}}
\def \cost{ \cos \frac{\theta}{2}}
%\newcommand{\sdot}{\mathbf{\bullet}}

\newcommand{\sdot}{{WI-WS, \delta \mv}}

\newcommand{\inty}{\int\limits_{-\infty}^{+\infty}}
\newcommand{\intyt}{\inty\inty\inty}
\newcommand{\intyV}{\int\limits_{V}}

\def\Rp{\mathcal{R}}
\def\Dp{\mathcal{D}}
\def\Tp{\mathcal{T}}
%\def\Cp{\mathcal{C}}
\def\Sp{\mathcal{S}}

% - Tariq's definitions begin here ==============================================================================
\def\beq{\begin{eqnarray}}
\def\eeq{\end{eqnarray}}

\def\mmbx#1{{\mathbf{#1}}}

\def\phi{\varphi}

\def\Vv{\mmbx{V}}
\def\gammav{\pmb{\gamma}}
\def\epsv{\pmb{\eps}}
\def\deltav{\pmb{\delta}}
\def\etav{\pmb{\eta}}

\def\v{V}
\def\rhov{\pmb{\rho}}
\def\r{\mmbx{r}}
\def\k{\mmbx{k}}

\def\d{\text{d}}
\def\c{\mmbx{c}}
\def\e{\mmbx{e}}
\def\m{\mmbx{m}}
\def\x{\mmbx{x}}
\def\xs{\x_s}
\def\xr{\x_r}
\def\L{\mmbx{L}}
\def\p{\mmbx{p}}
\def\q{\mmbx{q}}

\def\La{{\cal L}}
\def\tf{\tilde{f}}
\def\tA{\tilde{A}}
\def\ttau{\tilde{\tau}}
\def\y{\mmbx{y}}
\def\z{\mmbx{z}}

\def\tm{\tilde{m}}
\def\tr{\tilde{r}}
\def\tw{\tilde{w}}
\def\tv{\tilde{v}}
\def\tp{\tilde{p}}
\def\tq{\tilde{q}}

\def\a{\mmbx{a}}
\def\H{\mmbx{H}}
\def\g{\mmbx{g}}
\def\W{\mmbx{W}}

\def\eps{\varepsilon}

\def\La{{\cal L}}

\def\tlambda{\tilde{\lambda}}
\def\tw{\tilde{w}}

\def\rvn{r_{v_n}}
\def\rvh{r_{v_h}}
\def\rrho{r_\rho}
\def\rdel{r_\delta}
\def\reta{r_\eta}
\def\reps{r_\eps}


\def\Re{{{\cal{R}}_e}}

\newcommand{\pd}[2]{\frac{\partial #1}{\partial #2}}

%==============================================end of Tariq's notation=========================================


%%%%%%%%%								DEFINITIONS END
\newcommand{\mylabel}[1]{\label{#1}}
\newcommand{\myrf}[1]{\ref{#1}}

%%\newcommand{\plot}[3]{
%	\begin{figure}
%		\center
%		\includegraphics[#2]{Fig/#1}
%		\caption{#3}
%		\label{fig:#1}
%	\end{figure}
%}

\newcommand{\aplot}[3]{
	\begin{figure}[htbp!]
		\center
		\includegraphics[#2]{#1}
		\caption{#3}
		\label{fig:#1}
	\end{figure}
}

\newcommand{\twplot}[3]{
	\begin{figure}
		\centering
		\subfigure[]{\includegraphics[width=0.4\columnwidth]{Fig/#1}
			\label{fig:#1}}
		\hspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[width=0.55\columnwidth]{Fig/#2}
			\label{fig:#2}}
		\caption{#3}
		%\label{fig:#1}
	\end{figure}
}

\newcommand{\tplot}[4]{
	\begin{figure}
		\centering
		\subfigure[]{\includegraphics[width=0.45\columnwidth]{Fig/#1}
			\label{fig:#1}}
		\vspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[width=0.45\columnwidth]{Fig/#2}
			\label{fig:#2}}
		\vspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[width=0.65\columnwidth]{Fig/#3}
			\label{fig:#3}}
		\caption{#4}
		\label{fig:#1_#3}\label{fig:#1_Full}
	\end{figure}
}
\newcommand{\tplott}[4]{
	\begin{figure}
		\centering
		\subfigure[]{\includegraphics[width=0.2\columnwidth]{Fig/#1}
			\label{fig:#1}}
		\vspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[width=0.4\columnwidth]{Fig/#2}
			\label{fig:#2}}
		\vspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[width=0.3\columnwidth]{Fig/#3}
			\label{fig:#3}}
		\caption{#4}
		\label{fig:#1_#3}\label{fig:#1_Full}
	\end{figure}
}
\newcommand{\tplotv}[4]{
	\begin{figure}
		\centering
		\subfigure[]{\includegraphics[width=0.49\columnwidth]{Fig/#1}
			\label{fig:#1}}
		\vspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[width=0.49\columnwidth]{Fig/#2}
			\label{fig:#2}}
		\vspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[width=0.49\columnwidth]{Fig/#3}
			\label{fig:#3}}
		\caption{#4}
		\label{fig:#1_#3}\label{fig:#1_Full}
	\end{figure}
}

\newcommand{\ffplot}[5]{
	\begin{figure}
		\centering
		\subfigure[]{\includegraphics[width=0.3\columnwidth]{Fig/#1}
			\label{fig:#1}}
		%\hspace*{0.01\columnwidth}
		\subfigure[]{\includegraphics[width=0.3\columnwidth]{Fig/#2}
			\label{fig:#2}}
		%\hspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[width=0.3\columnwidth]{Fig/#3}
			\label{fig:#3}}
		%\hspace*{0.01\columnwidth}
		\subfigure[]{\includegraphics[width=0.9\columnwidth]{Fig/#4}
			\label{fig:#4}}
		\caption{#5}
		\label{fig:#1:#4}\label{fig:#1_Full}
		\vspace*{-0.03\columnwidth}
	\end{figure}
}

\newcommand{\fplot}[5]{
	\begin{figure}
		\centering
		\subfigure[]{\includegraphics[height=0.22\columnwidth]{Fig/#1}
			\label{fig:#1}}
		\hspace*{0.01\columnwidth}
		\subfigure[]{\includegraphics[height=0.3\columnwidth]{Fig/#2}
			\label{fig:#2}}
		\hspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[height=0.22\columnwidth]{Fig/#3}
			\label{fig:#3}}
		\hspace*{0.01\columnwidth}
		\subfigure[]{\includegraphics[height=0.22\columnwidth]{Fig/#4}
			\label{fig:#4}}
		\caption{#5}
		\label{fig:#1:#4}\label{fig:#1_Full}
		\vspace*{-0.03\columnwidth}
	\end{figure}
}

\newcommand{\splot}[7]{
	\begin{figure}
		\centering
		\subfigure[]{\includegraphics[height=0.27\columnwidth]{Fig/#1}
			\label{fig:#1}}
		\hspace*{0.01\columnwidth}
		\subfigure[]{\includegraphics[height=0.27\columnwidth]{Fig/#2}
			\label{fig:#2}}
		\hspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[height=0.27\columnwidth]{Fig/#3}
			\label{fig:#3}}
		\hspace*{0.01\columnwidth}
		\subfigure[]{\includegraphics[height=0.27\columnwidth]{Fig/#4}
			\label{fig:#4}}
		\subfigure[]{\includegraphics[height=0.27\columnwidth]{Fig/#5}
			\label{fig:#5}}
		\subfigure[]{\includegraphics[height=0.27\columnwidth]{Fig/#6}
			\label{fig:#6}}
		\caption{#7}
		\label{fig:#1:#6}\label{fig:#1_Full}
		\vspace*{-0.03\columnwidth}
	\end{figure}
}

\newcommand{\ssplot}[7]{
	\begin{figure}
		\centering
		\subfigure[]{\includegraphics[width=0.68\columnwidth]{Fig/#1}
			\label{fig:#1}}
		\hspace*{0.01\columnwidth}
		\subfigure[]{\includegraphics[width=0.68\columnwidth]{Fig/#2}
			\label{fig:#2}}
		\hspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[width=0.68\columnwidth]{Fig/#3}
			\label{fig:#3}}
		\\
		\vspace*{0.01\columnwidth}
		\subfigure[]{\includegraphics[width=0.25\columnwidth]{Fig/#4}
			\label{fig:#4}}
		\subfigure[]{\includegraphics[width=0.25\columnwidth]{Fig/#5}
			\label{fig:#5}}
		\subfigure[]{\includegraphics[width=0.25\columnwidth]{Fig/#6}
			\label{fig:#6}}
		\caption{#7}
		\label{fig:#1:#6}\label{fig:#1_Full}
		\vspace*{-0.03\columnwidth}
	\end{figure}
}

\newcommand{\fiPlot}[6]{
	\begin{figure}
		\centering
		\subfigure[]{\includegraphics[width=0.31\columnwidth]{Fig/#1}
			\label{fig:#1}}
		\hspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[width=0.31\columnwidth]{Fig/#2}
			\label{fig:#2}}
		\hspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[width=0.31\columnwidth]{Fig/#3}
			\label{fig:#3}}
		\hspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[width=0.33\columnwidth]{Fig/#4}
			\label{fig:#4}}
		\subfigure[]{\includegraphics[width=0.33\columnwidth]{Fig/#5}
			\label{fig:#5}}
		\caption{#6}
		\label{fig:#1:#5}\label{fig:#1_Full}
	\end{figure}
}

\newcommand{\dplot}[3]{
	\begin{figure}
		\centering
		\subfigure[]{\includegraphics[height=0.45\columnwidth]{Fig/#1}
			\label{fig:#1}}
		\hspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[height=0.45\columnwidth]{Fig/#2}
			\label{fig:#2}}
		\vspace*{-0.01\columnwidth}
		\caption{#3}
		\label{fig:#1:#2}\label{fig:#1_Full}
	\end{figure}
}

\newcommand{\ddplot}[3]{
	\begin{figure}
		\centering
		\subfigure[]{\includegraphics[width=0.7\columnwidth]{Fig/#1}
			\label{fig:#1}}
		\hspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[width=0.99\columnwidth]{Fig/#2}
			\label{fig:#2}}
		\vspace*{-0.01\columnwidth}
		\caption{#3}
		\label{fig:#1_#2}\label{fig:#1_Full}
	\end{figure}
}

\def\ewidth{0.4}


\newcommand{\eplot}[9]{
	\begin{figure}
		\centering
		\subfigure[]{\includegraphics[width=\ewidth\columnwidth]{Fig/#1}
			\label{fig:#1}}
		\hspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[width=\ewidth\columnwidth]{Fig/#2}
			\label{fig:#2}}
		\hspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[width=\ewidth\columnwidth]{Fig/#3}
			\label{fig:#3}}
		\hspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[width=\ewidth\columnwidth]{Fig/#4}
			\label{fig:#4}}
		\hspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[width=\ewidth\columnwidth]{Fig/#5}
			\label{fig:#5}}
		\hspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[width=\ewidth\columnwidth]{Fig/#6}
			\label{fig:#6}}
		\hspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[width=\ewidth\columnwidth]{Fig/#7}
			\label{fig:#7}}
		\hspace*{-0.01\columnwidth}
		\subfigure[]{\includegraphics[width=\ewidth\columnwidth]{Fig/#8}
			\label{fig:#8}}
		\caption{#9}
		%\label{fig:#1}
	\end{figure}
}

